South Africa's top court has rejected Olympian Oscar Pistorius' right to a last attempt to appeal against his conviction for the murder of girlfriend Reeva Steenkamp.

The verdict by the Constitutional Court on Thursday comes after the lower Supreme Court of Appeal upgraded the 29-year-old's conviction to murder in December from prior conviction of culpable homicide in the Pretoria High Court. He had been sentenced to five years in prison for culpable homicide.

South African authorities had challenged Pistorius' appeal on the grounds that the Supreme Court of Appeal had correctly found Pistorius guilty.

The athlete, nicknamed "Blade Runner" because of the prosthetic legs he uses to race, had filed papers to appeal against his conviction at the Constitutional Court on January 11.

National Prosecuting Authority spokesman Luvuyo Mfaku confirmed to international media that Oscar Pistorius' attempt to appeal has been denied.

Anneliese Burgess, the Pistorius' family spokeswoman, said she had just heard the news and would issue a statement after consulting with the family.

Steenkamp died on Valentine's Day in 2013 after being shot by Pistorius, who has spent the past few months under house arrest at his uncle's home in Pretoria while awaiting his appeal.

Pistorius now faces a possible minimum 15-year jail sentence for the murder of his girlfriend.

The 29-year-old is expected to be sentenced for murder - a crime carrying a minimum of 15 years in prison - in April.